Representations of Recursively Enumerable Array Languages by Contextual Array Grammars

Abstract

The main result proved in this paper shows that the natural embedding of any recursively enumerable one-dimensional array language in the two-dimensional space can be characterized by the projection of a two-dimensional array language generated by a contextual array grammar working in the t-mode and with norm one. Moreover, we show that any recursively enumerable one – dimensional array language can even be characterized by the projection of a two-dimensional array language generated by a contextual array grammar working in the t-mode where in the selectors of the contextual array productions only the ability to distinguish between blank and non-blank positions is necessary; in that case, the norm of the two-dimensional contextual array grammar working in the -mode cannot be bounded.